BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter C, Problem 36E
To determine

To calculate:

The value of x to satisfy the following inequality equation:

  sinx>cosx

Expert Solution

Answer to Problem 36E

The values of x for the interval [0,2π] to satisfy eq. sinx>cosx are [π4x5π4]

Explanation of Solution

Given information:

  sinx>cosx[0,2π]

Calculation:

Consider;

The unit circle with co-ordinates (x,y)=(cosx,sinx) and radius 1 to find out the values of x for the interval [0,2π] that cause sinx>cosx .

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter C, Problem 36E

Fig. Unit circle

From the figure;

  sinx>cosx , in the second quadrant x is negative and y is positive. So, in second quadrant the given inequality equation is satisfied.

In the fourth quadrant sinx>cosx , no value of x satisfy the inequality equation because sine is negative and cosine is positive here.

In the first quadrant, [π4xπ2] and in third quadrant [πx5π4]

Therefore, the values of x for the interval [0,2π] to satisfy eq. sinx>cosx are [π4x5π4]

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